# Algebra II : Solving and Graphing Logarithms

## Example Questions

### Example Question #71 : Solving And Graphing Logarithms

Solve .

Explanation:

The first thing we can do is combine all the log terms on the right side of the equation:

Next, we can take the coefficient from the left term and make it an exponent:

Now we can cancel the logs from both sides:

When we put  back into the original question, we don't have problems.  When we try it with  however, we get errors, so that's not a valid answer:

### Example Question #72 : Solving And Graphing Logarithms

Solve .

Explanation:

First, we take the coefficient, , and make it an exponent:

Now we can cancel the logs:

When we check our answers, however, we notice that  results in errors, so that's not a valid answer:

### Example Question #73 : Solving And Graphing Logarithms

Solve ,

Explanation:

First, we combine the log terms on the left of the equation:

Now we can cancel the logs on each side:

We can subtract  from each side to set the equation equal to .  this will give us a nice quadratic equation to solve:

Notice that  is not a valid answer, because if we plug it into the original equation then we would be taking the log of a negative number, which we can't do.  Our only solution is:

### Example Question #74 : Solving And Graphing Logarithms

Solve /

Explanation:

The first thing we can do is move both log functions to one side of the equation:

Then we can combine the log functions (remember, when you add logs, we multiply the terms inside):

Now we can rewrite the equation in exponent form (and FOIL the multiplied terms):

We can collect all the terms on one side of the equation, and then solve the quadratic:

However, if we plug  into the initial equation, we would be taking the log of a negative number, which we can't do, so it's not a valid solution:

### Example Question #75 : Solving And Graphing Logarithms

Solve .

Explanation:

We first put both logs on one side of the equation:

Now we combine the log terms (remember, when we subtract logs we divide the terms inside):

We can now rewrite the equation in exponential form:

Anything raised to the  power is , and now we can solve algebraically:

### Example Question #76 : Solving And Graphing Logarithms

Solve .

Explanation:

We start by rewriting the equation in exponential form:

Now we can simplify:

### Example Question #77 : Solving And Graphing Logarithms

Solve .

Explanation:

We can either do this the long and proper way, or the simple and easy way.

The long way:

First, we move both logs to the same side of the equation:

Now we can combine the logs (reminder, when you subtract logs, you divide the terms inside of them):

Let's rewrite the equation in exponential form:

Anything raised to the  power equals , so we can simplify and solve from here:

The short way:

First, we cancel the log terms (because the base is the same, and all we have are the log terms):

Then we divide by :

### Example Question #78 : Solving And Graphing Logarithms

= _______

Explanation:

is equal to ,

so in this case it is

,

and

### Example Question #1 : Graphing Logarithmic Functions

Give the -intercept of the graph of the function

to two decimal places.

The graph has no -intercept.

Explanation:

Set  and solve:

The -intercept is .

### Example Question #2 : Graphing Logarithmic Functions

Give the  intercept of the graph of the function

to two decimal places.